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Kai Du

Publications and source records attributed to Kai Du.

At least 55 records · Page 3Linked to original sources
arXiv2023

Topological Surface Magnetism and Neel Vector Control in a Magnetoelectric Antiferromagnet

Antiferromagnetic states with no stray magnetic fields can enable high-density ultra-fast spintronic technologies. However, the detection and control of antiferromagnetic Neel vectors remain challenging. Linear magnetoelectric antiferromagnets (LMAs) may provide new pathways, but applying simultaneous electric and magnetic fields, necessary to control Neel vectors in LMAs, is cumbersome and impractical for most applications. Herein, we show that Cr2O3, a prototypical room-temperature LMA, carries a topologically-protected surface magnetism in all surfaces, which stems from intrinsic surface electric fields due to band bending, combined with the bulk linear magnetoelectricity. Consequently, bulk Neel vectors with zero bulk magnetization can be simply tuned by magnetic fields through controlling the magnetizations associated with the surface magnetism. Our results imply that the surface magnetizations discovered in Cr2O3 should be also present in all LMAs.

cond-mat.mtrl-sci↗
arXiv2023

Sequential propagation of chaos

A new class of particle systems with sequential interaction is proposed to approximate the McKean-Vlasov process that originally arises as the limit of the mean-field interacting particle system. The weighted empirical measure of this particle system is proved to converge to the law of the McKean-Vlasov process as the system grows. Based on the Wasserstein metric, quantitative propagation of chaos results are obtained for two cases: the finite time estimates under the monotonicity condition and the uniform in time estimates under the dissipation and the non-degenerate conditions. Numerical experiments are implemented to demonstrate the theoretical results.

math.PR↗
arXiv2021

Empirical approximation to invariant measures for McKean--Vlasov processes: mean-field interaction vs self-interaction

This paper proves that, under a monotonicity condition, the invariant probability measure of a McKean--Vlasov process can be approximated by weighted empirical measures of some processes including itself. These processes are described by distribution dependent or empirical measure dependent stochastic differential equations constructed from the equation for the McKean--Vlasov process. Convergence of empirical measures is characterized by upper bound estimates for their Wasserstein distance to the invariant measure. The theoretical results are demonstrated via a mean-field Ornstein--Uhlenbeck process.

math.PR↗
arXiv2021

Efficient light-emitting diodes based on oriented perovskite nanoplatelets

Solution-processed planar perovskite light-emitting diodes (LEDs) promise high-performance and cost-effective electroluminescent (EL) devices ideal for large-area display and lighting applications. Exploiting emission layers with high ratios of horizontal transition dipole moments (TDMs) is expected to boost photon outcoupling of planar LEDs. However, LEDs based on anisotropic perovskite nanoemitters remains to be inefficient (external quantum efficiency, EQE <5%), due to the difficulties of simultaneously controlling the orientations of TDMs, achieving high photoluminescence quantum yields (PLQYs) and realizing charge balance in the films of the assembled nanostructures. Here we demonstrate efficient EL from an in-situ grown continuous perovskite film comprising of a monolayer of face-on oriented nanoplatelets. The ratio of horizontal TDMs of the perovskite nanoplatelet films is ~84%, substantially higher than that of isotropic emitters (67%). The nanoplatelet film shows a high PLQY of ~75%. These merits enable LEDs with a peak EQE of 23.6%, representing the most efficient perovskite LEDs.

physics.app-ph↗
arXiv2021

Permutable SOS (Symmetry Operational Similarity)

Based on symmetry consideration, quasi-one-dimensional (1D) objects, relevant to numerous observables or phenomena, can be classified into eight different types. We provide various examples of each 1D type, and discuss their Symmetry Operational Similarity (SOS) relationships, which are often permutable. A number of recent experimental observations, including current-induced magnetization in polar or chiral conductors, non-linear Hall effect in polar conductors, spin-polarization of tunneling current to chiral conductors, and ferro-rotational domain imaging with linear gyration are discussed in terms of (permutable) SOS. In addition, based on (permutable) SOS, we predict a large number of new phenomena in low symmetry materials that can be experimentally verified in the future.

cond-mat.mes-hall↗
arXiv2020

A Q-learning algorithm for discrete-time linear-quadratic control with random parameters of unknown distribution: convergence and stabilization

This paper studies an infinite horizon optimal control problem for discrete-time linear systems and quadratic criteria, both with random parameters which are independent and identically distributed with respect to time. A classical approach is to solve an algebraic Riccati equation that involves mathematical expectations and requires certain statistical information of the parameters. In this paper, we propose an online iterative algorithm in the spirit of Q-learning for the situation where only one random sample of parameters emerges at each time step. The first theorem proves the equivalence of three properties: the convergence of the learning sequence, the well-posedness of the control problem, and the solvability of the algebraic Riccati equation. The second theorem shows that the adaptive feedback control in terms of the learning sequence stabilizes the system as long as the control problem is well-posed. Numerical examples are presented to illustrate our results.

math.OC↗
arXiv2020

Human Perception-based Evaluation Criterion for Ultra-high Resolution Cell Membrane Segmentation

Computer vision technology is widely used in biological and medical data analysis and understanding. However, there are still two major bottlenecks in the field of cell membrane segmentation, which seriously hinder further research: lack of sufficient high-quality data and lack of suitable evaluation criteria. In order to solve these two problems, this paper first proposes an Ultra-high Resolution Image Segmentation dataset for the Cell membrane, called U-RISC, the largest annotated Electron Microscopy (EM) dataset for the Cell membrane with multiple iterative annotations and uncompressed high-resolution raw data. During the analysis process of the U-RISC, we found that the current popular segmentation evaluation criteria are inconsistent with human perception. This interesting phenomenon is confirmed by a subjective experiment involving twenty people. Furthermore, to resolve this inconsistency, we propose a new evaluation criterion called Perceptual Hausdorff Distance (PHD) to measure the quality of cell membrane segmentation results. Detailed performance comparison and discussion of classic segmentation methods along with two iterative manual annotation results under existing evaluation criteria and PHD is given.

cs.CV↗
arXiv2020

Highly tunable ferroelectricity in hybrid improper ferroelectric Sr3Sn2O7

The successful theoretical prediction and experimental demonstration of hybrid improper ferroelectricity (HIF) provides a new pathway to couple octahedral rotations, ferroelectricity, and magnetism in complex materials. To enable technological applications, a HIF with a small coercive field is desirable. We successfully grow Sr3Sn2O7 single crystals, and discover that they exhibit the smallest electric coercive field at room temperature among all known HIFs. Furthermore, we demonstate that a small external stress can repeatedly erase and re-generate ferroelastic domains. In addition, using in-plane piezo-response force microscopy, we characterize abundant charged and neutral domain walls. The observed small electrical and mechanical coercive field values are in accordance with the results of our first-principles calculations on Sr3Sn2O7, which show low energy barriers for both 90° and 180° polarization switching compared to those in other experimentally demonstrated HIFs. Our findings represent an advance towards the possible technological implemetation of functional HIFs.

cond-mat.mtrl-sci↗
arXiv2020

Direct Visualization of Irreducible Ferrielectricity in Crystals

In solids, charge polarity can one-to-one correspond to spin polarity phenomenologically, e.g. ferroelectricity/ferromagnetism, antiferroelectricity/antiferromagnetism, and even dipole-vortex/magnetic-vortex, but ferrielectricity/ferrimagnetism kept telling a disparate story in microscopic level. Since the definition of a charge dipole involves more than one ion, there may be multiple choices for a dipole unit, which makes most ferrielectric orders equivalent to ferroelectric ones, i.e. this ferrielectricity is not necessary to be a real independent branch of polarity. In this work, by using the spherical aberration-corrected scanning transmission electron microscope, we visualize a nontrivial ferrielectric structural evolution in BaFe2Se3, in which the development of two polar sub-lattices is out-of-sync, for which we term it as irreducible ferrielectricity. Such irreducible ferrielectricity leads to a non-monotonic behavior for the temperature-dependent polarization, and even a compensation point in the ordered state. Our finding unambiguously distinguishes ferrielectrics from ferroelectrics in solids.

cond-mat.mtrl-sci↗
arXiv2019

Krylov-Safonov estimates for a degenerate diffusion process

This paper proves a Krylov-Safonov estimate for a multidimensional diffusion process whose diffusion coefficients are degenerate on the boundary. As applications the existence and uniqueness of invariant probability measures for the process and Hoelder estimates for the associated partial differential equation are obtained.

math.PR↗
arXiv2019

Schauder-type estimates for higher-order parabolic SPDEs

In this paper we consider the Cauchy problem for $2m$-order stochastic partial differential equations of parabolic type in a class of stochastic Hoelder spaces. The Hoelder estimates of solutions and their spatial derivatives up to order $2m$ are obtained, based on which the existence and uniqueness of solution is proved. An interesting finding of this paper is that the regularity of solutions relies on a coercivity condition that differs when $m$ is odd or even: the condition for odd $m$ coincides with the standard parabolicity condition in the literature for higher-order stochastic partial differential equations, while for even $m$ it depends on the integrability index $p$. The sharpness of the new-found coercivity condition is demonstrated by an example.

math.PR↗
arXiv2018

The role of protection zone on species spreading governed by a reaction-diffusion model with strong Allee effect

It is known that a species dies out in the long run for small initial data if its evolution obeys a reaction of bistable nonlinearity. Such a phenomenon, which is termed as the strong Allee effect, is well supported by numerous evidence from ecosystems, mainly due to the environmental pollution as well as unregulated harvesting and hunting. To save an endangered species, in this paper we introduce a protection zone that is governed by a Fisher-KPP nonlinearity, and examine the dynamics of a reaction-diffusion model with strong Allee effect and protection zone. We show the existence of two critical values $0<L_*\leq L^*$, and prove that a vanishing-transition-spreading trichotomy result holds when the length of protection zone is smaller than $L_*$; a transition-spreading dichotomy result holds when the length of protection zone is between $L_*$ and $L^*$; only spreading happens when the length of protection zone is larger than $L^*$. This suggests that the protection zone works when its length is larger than the critical value $L_*$. Furthermore, we compare two types of protection zone with the same length: a connected one and a separate one, and our results reveal that the former is better for species spreading than the latter.

math.AP↗
arXiv2018

First Investigation on the Radiation Field of the Gas-Filled Three-Axis Cylindrical Hohlraum

A novel ignition hohlraum named three-axis cylindrical hohlraum (TACH) is designed for indirect-drive inertial confinement fusion. TACH is a kind of 6 laser entrance holes (LEHs) hohlraum, which is orthogonally jointed of three cylindrical hohlraums. The first experiment on the radiation field of TACH was performed on Shenguang III laser facility. 24 laser beams were elected and injected into 6 LEHs quasi-symmetrically. Total laser energy was about 59 kJ, and the peak radiation temperature reached about 192 eV. Radiation temperature and pinhole images in gas-filled hohlraum are largely identical but with minor differences with those in vacuum hohlraum. All laser energy can be totally delivered into hohlraum in 3 ns duration even without filled gas in the hohlraum of 1.4 mm diameter. Plasma filling cannot be obviously suppressed even with 0.5 atm pressure gas in the small hohlraum. Backscattering fractions of vacuum hohlraum and gas-filled hohlraum are both lower than 2%. Experimental study of this new kind of hohlraum can provide guidance for future target design and implosion experiment.

physics.plasm-ph↗
arXiv2018

A simple blind-denoising filter inspired by electrically coupled photoreceptors in the retina

Photoreceptors in the retina are coupled by electrical synapses called "gap junctions". It has long been established that gap junctions increase the signal-to-noise ratio of photoreceptors. Inspired by electrically coupled photoreceptors, we introduced a simple filter, the PR-filter, with only one variable. On BSD68 dataset, PR-filter showed outstanding performance in SSIM during blind denoising tasks. It also significantly improved the performance of state-of-the-art convolutional neural network blind denosing on non-Gaussian noise. The performance of keeping more details might be attributed to small receptive field of the photoreceptors.

cs.CV↗
arXiv2018

Microwave Conductivity of Ferroelectric Domains and Domain Walls in Hexagonal Rare-earth Ferrite

We report the nanoscale electrical imaging results in hexagonal $Lu_{0.6}Sc_{0.4}FeO_3$ single crystals using conductive atomic force microscopy (C-AFM) and scanning microwave impedance microscopy (MIM). While the dc and ac response of the ferroelectric domains can be explained by the surface band bending, the drastic enhancement of domain wall (DW) ac conductivity is clearly dominated by the dielectric loss due to DW vibration rather than mobile-carrier conduction. Our work provides a unified physical picture to describe the local conductivity of ferroelectric domains and domain walls, which will be important for future incorporation of electrical conduction, structural dynamics, and multiferroicity into high-frequency nano-devices.

cond-mat.mtrl-sci↗
arXiv2018

Vortex Ferroelectric Domains, Large-loop Weak Ferromagnetic Domains, and Their Decoupling in Hexagonal (Lu, Sc)FeO3

The direct domain coupling of spontaneous ferroelectric polarization and net magnetic moment can result in giant magnetoelectric (ME) coupling, which is essential to achieve mutual control and practical applications of multiferroics. Recently, the possible bulk domain coupling, the mutual control of ferroelectricity (FE) and weak ferromagnetism (WFM) have been theoretically predicted in hexagonal LuFeO3. Here, we report the first successful growth of highly-cleavable Sc-stabilized hexagonal Lu0.6Sc0.4FeO3 (h-LSFO) single crystals, as well as the first visualization of their intrinsic cloverleaf pattern of vortex FE domains and large-loop WFM domains. The vortex FE domains are on the order of 0.1-1 μm in size. On the other hand, the loop WFM domains are ~100 μm in size, and there exists no interlocking of FE and WFM domain walls. These strongly manifest the decoupling between FE and WFM in h-LSFO. The domain decoupling can be explained as the consequence of the structure-mediated coupling between polarization and dominant in-plane antiferromagnetic spins according to the theoretical prediction, which reveals intriguing interplays between FE, WFM, and antiferromagnetic orders in h-LSFO. Our results also indicate that the magnetic topological charge tends to be identical to the structural topological charge. This could provide new insights into the induction of direct coupling between magnetism and ferroelectricity mediated by structural distortions, which will be useful for the future applications of multiferroics.

cond-mat.mtrl-sci↗
arXiv2018

Stochastic continuity of random fields governed by a system of stochastic PDEs

This paper constructs a solvability theory for a system of stochastic partial differential equations. On account of the Kolmogorov continuity theorem, solutions are looked for in certain Hölder-type classes in which a random field is treated as a space-time function taking values in $L^{p}$-space of random variables. A modified stochastic parabolicity condition involving $p$ is proposed to ensure the finiteness of the associated norm of the solution, which is showed to be sharp by examples. The Schauder-type estimates and the solvability theorem are proved.

math.PR↗